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PSAT Math : How to add exponents

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Example Question #11 : Exponential Operations

If $3^{4x+6}=27^{2x}$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Using exponents, 27 is equal to 3³. So, the equation can be rewritten:

3^{4x + 6} = (3³)^2x

3^{4x + 6} = 3^6x

When both side of an equation have the same base, the exponents must be equal. Thus:

4x + 6 = 6x

6 = 2x

x = 3

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Example Question #81 : Exponents

What is the value of such that 2^n=4^2*16^3*32^2 ?

Possible Answers:

240

480

Correct answer:

Explanation:

We can solve by converting all terms to a base of two. 4, 16, and 32 can all be expressed in terms of 2 to a standard exponent value.

$4=2^2\rightarrow 4^2=(2^2)^2$

$16=2^4\rightarrow 16^3=(2^4)^3$

$32=2^5\rightarrow 32^2=(2^5)^2$

We can rewrite the original equation in these terms.

2^n=(2^2)^2*(2^4)^3*(2^5)^2

Simplify exponents.

$2^n=(2^4)*(2^{12})*(2^{10})$

Finally, combine terms.

$2^n=2^{4+12+10}=2^{26}$

From this equation, we can see that n=26 .

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Example Question #11 : Exponents

How many of the following base ten numbers have a base five representation of exactly four digits?

(A) 100

(B) 200

(D) 400

Possible Answers:

Four

None

One

Two

Three

Correct answer:

Three

Explanation:

A number in base five has powers of five as its place values; starting at the right, they are $1, 5 ^{1} = 5, 5 ^{2} = 25, 5 ^{3} = 125,5 ^{4} = 125$

The lowest base five number with four digits would be

$1000 _{\textrm{five}} = 1 \times 5^{3} = 125$ in base ten.

The lowest base five number with five digits would be

$10000 _{\textrm{five}} = 1 \times 5^{4} = 625$ in base ten.

Therefore, a number that is expressed as a four-digit number in base five must fall in the range

$125 \leq N \leq 624$

Three of the four numbers - all except 100 - fall in this range.

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Example Question #11 : Exponents

Solve for $x$ :

$4^{4}+4^{4}+4^{4}+4^{4}=2^{x}$

Possible Answers:

$9$

$6$

$8$

$11$

$10$

Correct answer:

$10$

Explanation:

Combining the powers, we get $1024=2^{x}$ .

From here we can use logarithms, or simply guess and check to get $x=10$ .

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Example Question #11 : Exponents

If $\dpi{100} \small r$ and $\dpi{100} \small s$ are positive integers, and $\dpi{100} \small 25\left ( 5^{r} \right )=5^{s-2}$ , then what is $\dpi{100} \small s$ in terms of $\dpi{100} \small r$ ?

Possible Answers:

$\dpi{100} \small r+4$

$\dpi{100} \small r$

$\dpi{100} \small r+3$

$\dpi{100} \small r+1$

$\dpi{100} \small r+2$

Correct answer:

$\dpi{100} \small r+4$

Explanation:

$\dpi{100} \small 25\left ( 5^{r} \right )$ is equal to $5^{2}\left ( 5^{r}\right )$ which is equal to $\dpi{100} \small \left ( 5^{r+2} \right )$ . If we compare this to the original equation we get $\dpi{100} \small r+2=s-2\rightarrow s=r+4$

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PSAT Math : How to add exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #11 : Exponential Operations

Example Question #81 : Exponents

Example Question #11 : Exponents

Example Question #11 : Exponents

Example Question #11 : Exponents

All PSAT Math Resources

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