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PSAT Math : How to multiply exponents

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Example Question #51 : Exponential Operations

If and are nonzero numbers such that a^2 = b^3 , which of the following is equivalent to a^6 ?

Possible Answers:

$b^{11}$

b^9

b^7

b^8

b^6

Correct answer:

b^9

Explanation:

For this problem, we need to make use of the property of exponents, which states that (x^y)^z = x^y^z.

We are given a² but are asked to find a⁶.

Let's raise both sides of the equation to the third power, so that we will end up with a⁶ on the left side.

(a²)³ = (b³)³

Now, according to the property of exponents mentioned before, we can multiply the exponents.

a^(2*3) = b^(3*3)

a⁶ = b⁹

The answer is b⁹.

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Example Question #21 : Exponents

If and are positive integers and $2^{2a}(2^{2b})=16$ , what is the value of a +b ?

Possible Answers:

Correct answer:

Explanation:

The question tells us that 2^2a ( 2^2b)= 16.

We can rewrite 16 as 2⁴, giving us 2^2a ( 2^2b)= 2⁴.

When terms with the same base are multipled, their exponents can be added:

2^{(2a +2b)}= 2⁴

Since the base is the same on both sides of the equation, we can equate the exponents:

2a +2b = 4

2(a + b) = 4

a + b = 2

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Example Question #51 : Exponents

Simplify:

$\left ( \frac{x}{2t^{2}} \right )^{3}$

Possible Answers:

$\frac{x^{3}}{ 9t^{6} }$

$\frac{ 8 t^{6} }{x^{3}}$

$\frac{x^{3}}{ 6 t^{6} }$

$\frac{ 6 t^{6} }{x^{3}}$

$\frac{x^{3}}{ 8 t^{6} }$

Correct answer:

$\frac{x^{3}}{ 8 t^{6} }$

Explanation:

Apply the the various properties of exponents:

$\left ( \frac{x}{2t^{2}} \right )^{3}$

$=\frac{x^{3}}{ \left ( 2t^{2} \right ) ^{3}}$

$=\frac{x^{3}}{ 2^{3} \left ( t^{2} \right )^{3} }$

$=\frac{x^{3}}{ 8 t^{2 \cdot 3} }$

$=\frac{x^{3}}{ 8 t^{6} }$

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Example Question #22 : How To Multiply Exponents

$\textup{If }4^{3}\times8^{2}=2^{y}\textup{, what is the value of }y\textup{ ?}$

Possible Answers:

Correct answer:

Explanation:

$\textup{4 and 8 are powers of 2. Find the common base and set exponents equal:}$

$\left ( 2^{2}\right )^{3}\times \left ( 2^{3}\right )^{2}=2^{y}\: \; \; \; \; \; \;2^{6}\times 2^{6}=2^{y}$

$2^{12}=2^{y}\: \: \: \: \: \: \:12=y$

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Example Question #61 : Exponential Operations

Simplify: $x^{5}\cdot x^{2}$

Possible Answers:

$2x^{7}$

$x^{7}$

$2x^{10}$

$x^{10}$

This expression cannot be simplified any further

Correct answer:

$x^{7}$

Explanation:

When you are multiplying and the bases are the same, you add the exponents together. Because both bases are you add 5+2=7 as your new exponent. You then keep the same base, , to the 7th power.

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Example Question #24 : How To Multiply Exponents

Solve for :

$\sqrt[3]{x-3} = 2$

Possible Answers:

$None\ of\ the\ above$

Correct answer:

Explanation:

$\left ( \sqrt[3]{x-3} \right )^{3} = 2^{3}$

Now the left side equals x-3 and the right side equals 8. Hence:

x-3 = 8

Therefore must be equal to 11.

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PSAT Math : How to multiply exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #51 : Exponential Operations

Example Question #21 : Exponents

Example Question #51 : Exponents

Example Question #22 : How To Multiply Exponents

Example Question #61 : Exponential Operations

Example Question #24 : How To Multiply Exponents

All PSAT Math Resources

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