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ISEE Upper Level Math : How to multiply exponents

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Example Questions

Example Question #11 : How To Multiply Exponents

What is the value of this equation?

$(x^{2})^{3}-(2^{3})^{2}$ $\displaystyle (x^{2})^{3}-(2^{3})^{2}$

Possible Answers:

$x^{6}-64$ $\displaystyle x^{6}-64$

$x^{6}-32$ $\displaystyle x^{6}-32$

$x^{5}-64$ $\displaystyle x^{5}-64$

$x^{6}+64$ $\displaystyle x^{6}+64$

Correct answer:

$x^{6}-64$ $\displaystyle x^{6}-64$

Explanation:

When an exponent is raised to another exponent, the exponents should be multiplied toghether. This will result in:

$(x^{2})^{3}-(2^{3})^{2}$ $\displaystyle (x^{2})^{3}-(2^{3})^{2}$

$x^{6}-2^{6}$ $\displaystyle x^{6}-2^{6}$

$x^{6}-64$ $\displaystyle x^{6}-64$

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Example Question #12 : How To Multiply Exponents

Which expression is equal to $(x^{2})^{3}$ $\displaystyle (x^{2})^{3}$ ?

Possible Answers:

$x^{\frac{2}{3}}$ $\displaystyle x^{\frac{2}{3}}$

$x^{5}$ $\displaystyle x^{5}$

$x^{6}$ $\displaystyle x^{6}$

$x^{\frac{3}{2}}$ $\displaystyle x^{\frac{3}{2}}$

Correct answer:

$x^{6}$ $\displaystyle x^{6}$

Explanation:

When exponent of a value is raised to another exponent, the values of the exponents are multiplied by each other.

$(x^{2})^{3}$ $\displaystyle (x^{2})^{3}$

2 is multiplied by 3, and so the exponent of x is 6.

$x^{6}$ $\displaystyle x^{6}$

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Example Question #13 : How To Multiply Exponents

What is the value of $(2^{6})^{\frac{1}{2}}$ $\displaystyle (2^{6})^{\frac{1}{2}}$ ?

Possible Answers:

$\displaystyle 8$

$\displaystyle 32$

$\displaystyle 16$

$\displaystyle 4$

Correct answer:

$\displaystyle 8$

Explanation:

When one exponent is raised to another exponent, the values of the exponents should be multiplied together. Thus,

$(2^{6})^{\frac{1}{2}}$ $\displaystyle (2^{6})^{\frac{1}{2}}$ can be simplified to $2^{3}$ $\displaystyle 2^{3}$ , given that $6\cdot \frac{1}{2}=3$ $\displaystyle 6\cdot \frac{1}{2}=3$ .

$2^{3}=2\cdot2\cdot2=8$ $\displaystyle 2^{3}=2\cdot2\cdot2=8$

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Example Question #14 : How To Multiply Exponents

What is the expression below equal to?

$3x^{4}*5x^{9}$ $\displaystyle 3x^{4}*5x^{9}$

Possible Answers:

$8x^{9}$ $\displaystyle 8x^{9}$

$15x^{13}$ $\displaystyle 15x^{13}$

$8x^{36}$ $\displaystyle 8x^{36}$

$15x^{36}$ $\displaystyle 15x^{36}$

Correct answer:

$15x^{13}$ $\displaystyle 15x^{13}$

Explanation:

When exponents are multiplied by each other, the powers should be added together. Meanwhile, numbers not raised to an exponent are simply multiplied by each other.

Therefore, the answer is $15x^{13}$ $\displaystyle 15x^{13}$ , because 3*5=15 $\displaystyle 3*5=15$ , and 9+4=13 $\displaystyle 9+4=13$ .

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Example Question #15 : How To Multiply Exponents

What is the value of $-1^{323}$ $\displaystyle -1^{323}$ ?

Possible Answers:

323 $\displaystyle 323$

$\displaystyle -1$

$\displaystyle -323$

$\displaystyle 1$

Correct answer:

$\displaystyle -1$

Explanation:

1 raised to any exponent will always be 1.

-1 will be equal to 1 when the exponent is even and will be equal to -1 when the exponent is odd.

Given that 323 is odd, $-1^{323}$ $\displaystyle -1^{323}$ is equal to -1.

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Example Question #516 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify the following:

$\displaystyle 6x^5*5x^6*3x^2$

Possible Answers:

$33x^{11}$ $\displaystyle 33x^{11}$

$14x^{90}$ $\displaystyle 14x^{90}$

$90x^{13}$ $\displaystyle 90x^{13}$

$45x^{7}$ $\displaystyle 45x^{7}$

Correct answer:

$90x^{13}$ $\displaystyle 90x^{13}$

Explanation:

Simplify the following:

$\displaystyle 6x^5*5x^6*3x^2$

Let's begin by recalling two rules

1) When multiplying variables with a common base, add the exponents.

2) When multiplying variables with a common base, multiply the coefficients.

$6x^5*5x^6*3x^2=(5*6*3)x^{5+6+2}=90x^{13}$ $\displaystyle 6x^5*5x^6*3x^2=(5*6*3)x^{5+6+2}=90x^{13}$

So, our answer is

$90x^{13}$ $\displaystyle 90x^{13}$

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : How to multiply exponents

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #11 : How To Multiply Exponents

Example Question #12 : How To Multiply Exponents

Example Question #13 : How To Multiply Exponents

Example Question #14 : How To Multiply Exponents

Example Question #15 : How To Multiply Exponents

Example Question #516 : Isee Upper Level (Grades 9 12) Mathematics Achievement

All ISEE Upper Level Math Resources

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