Exponential Operations

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ACT Math › Exponential Operations

Questions 1 - 10

What is the value of m where:

$64^{\frac{n}{12}}=(m)4^{(\frac{1+m}{m+n})}$

-2

Explanation

If n=4, then 64(4/12)=64(1/3)=4. Then, 4=m4(1+m)/(m+4). If 2 is substituted for m, then 4=24(1+2)/(2+4)=241/2=2√4=22=4.

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

Cannot be determined

Explanation

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

$64^{\frac{4}{3}}$ can be written as which of the following?

A. $\sqrt[3]{64^4}$

B. $(\sqrt[3]{64})^{4}$

A, B and C

B and C

A and C

C only

B only

Explanation

C is computing the exponent, while A and B are equivalent due to properties of fractional exponents.

Remember that...

$a^{\frac{b}{c}} = \sqrt[c]{a^b} = (\sqrt[c]{a})^b$

$64^{\frac{4}{3}}=$ $\sqrt[3]{64^4}=$ $(\sqrt[3]{64})^{4}=$

Solve for :

$\frac{64^4}{8^x} = 8$

Explanation

First, reduce all values to a common base using properties of exponents.

Plugging back into the equation-

$8^8 = 8^x\cdot 8^1$

Using the formula

$x^a\cdot x^b=x ^{a+b}$

We can reduce our equation to

So,

Simplify the following: $x^{5}\cdot x^{5}$

$x^{10}$

$x^{25}$

$x^{225}$

$x^{5}$

$x^{15}$

Explanation

When two variables with exponents are multiplied, you can simplify the expression by adding the exponents together. In this particular problem, the correct answer is found by adding the exponents 5 and 5, yielding $x^{10}$ .