GRE Math : How to multiply exponents

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Example Questions

Example Question #24 : How To Multiply Exponents

Simplify:

$(6x^{2})^{3}\cdot x^{-7}\cdot 2x^{4}$

Possible Answers:

$6x^{2}$

$432x^{3}$

$12x^{2}$

Correct answer:

$432x^{3}$

Explanation:

Remember, we add exponents when their bases are multiplied, and multiply exponents when one is raised to the power of another. Negative exponents flip to the denominator (presuming they originally appear in the numerator).

$(6x^{2})^{3}\cdot x^{-7}\cdot 2x^{4}$

$=\frac{216x^{6}\cdot 2x^{4}}{x^{7}}$

$=\frac{432x^{10}}{x^{7}}$

$=432x^{3}$

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Example Question #71 : Exponents

is a real number such that $y\geq 1$ .

Quantity A: (y^2)(y^4)

Quantity B: y^8

Possible Answers:

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

Quantity B is greater.

Correct answer:

The relationship cannot be determined from the information given.

Explanation:

(y²)(y⁴) = y²⁺⁴ = y⁶

Plug in two different values for y.

Plug in y = 1: y⁸ = y⁶

Plug in y = 2: y⁸ > y⁶

Since the results differ, the relationship cannot be determined from the information given.

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Example Question #712 : Algebra

Evaluate:

$y=\frac{3^{13}-9^{5}}{\left ( \frac{1}{27} \right )^{-3}}$

Possible Answers:

$\dpi{100} \small 81$

$\dpi{100} \small 27$

$\dpi{100} \small 78$

$\dpi{100} \small 24$

$\dpi{100} \small 30$

Correct answer:

$\dpi{100} \small 78$

Explanation:

Can be simplified to:

Capture2

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Example Question #72 : Exponents

Simplify the following expression.

$\frac{((x^4)^{-7})}{(x^2*x^4)}$

Possible Answers:

$\frac{1}{x^{34}}$

$x^{22}$

$x^{34}$

$\textup{This expression can't be simplified any further}$

$\frac{1}{x^{22}}$

Correct answer:

$\frac{1}{x^{34}}$

Explanation:

To solve this problem, we must first understand some of the basic concepts of exponents. When multiplying exponents with the same base, one would simply add the powers together with the same base to obtain the result. For example, $x^a*x^b=x^{a+b}$ .

When raising exponents to a certain power, one would simply multiply the power the exponent is being raised to with the exponent itself to obtain the new exponent. The base also gets raised to the same power as it normally would and the new exponent gets put on afterward. For example $({x^a})^{b}=x^{a*b}$ .

Now that we have covered the basic concepts of exponent manipulation, we can now solve the problem. The top part of the expression give to us is $((x^4)^{-7})$ . As we have stated before, when an exponent is raised to a certain power, you simply multiply the power and the exponent together. This results in $x^{4*-7}=x^{-28}$ .

The new expression becomes $\frac{x^{-28}}{(x^2*x^4)}$ .

Solving for the denominator of the equation, we previously stated that when multiplying exponents together with the same base, we simply add the exponents together and keep the same base. Therefore $(x^2*x^4)=x^{2+4}=x^6$ .

The new expression becomes $\frac{x^{-28}}{x^6}$ , however $x^{-28}=\frac{1}{x^{28}}$ , therefore the expression becomes $\frac{1}{x^{28}*x^{6}}=\frac{1}{x^{34}}$ .

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GRE Math : How to multiply exponents

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #24 : How To Multiply Exponents

Example Question #71 : Exponents

Example Question #712 : Algebra

Example Question #72 : Exponents

All GRE Math Resources

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