((4^(0))^(-3))/(4^(-3))

Simplify numerator: Simplify the numerator using the property that any non-zero number raised to the power of 0 is 1. ((4^(0))^(-3)) = (1)^(-3)Simplify denominator: Simplify the denominator using the property of negative exponents which states that a^(-n) = 1/(a^n). 4^(-3) = 1/(4^3)Substitute and simplify: Substitute the simplified numerator and denominator into the original expression. ((4^(0))^(-3))/(4^(-3)) = (1)^(-3) / (1/(4^3))Recognize and simplify: Simplify the expression by recognizing that (1)^(-3) is just 1, because any number to the power of -3 is the reciprocal of that number to the power of 3, and the reciprocal of 1 is still 1. (1)^(-3) = 1Multiply by reciprocal: Now, we have 1 divided by (1/(4^3)), which is the same as multiplying by the reciprocal. 1 / (1/(4^3)) = 1 * (4^3)Perform multiplication: Perform the multiplication to get the final answer. 1 * (4^3) = 4^3Calculate final answer: Calculate the value of 4^3. 4^3 = 4 * 4 * 4 = 64

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\frac{\left(4^{0}\right)^{-3}}{4^{-3}}$

View step-by-step help

Home

Math Problems

Algebra 2

Evaluate rational exponents

Full solution

\frac{\left(4^{0}\right)^{-3}}{4^{-3}}

Simplify numerator: Simplify the numerator using the property that any non-zero number raised to the power of $0$ is $1$ . $\left(4^{0}\right)^{-3} = \left(1\right)^{-3}$
Simplify denominator: Simplify the denominator using the property of negative exponents which states that $a^{-n} = \frac{1}{a^n}$ . $\newline$ $4^{-3} = \frac{1}{4^3}$
Substitute and simplify: Substitute the simplified numerator and denominator into the original expression. $\left(4^{0}\right)^{-3}/4^{-3} = 1^{-3} / \left(1/4^{3}\right)$
Recognize and simplify: Simplify the expression by recognizing that $(1)^{-3}$ is just $1$ , because any number to the power of $-3$ is the reciprocal of that number to the power of $3$ , and the reciprocal of $1$ is still $1$ . $(1)^{-3} = 1$
Multiply by reciprocal: Now, we have $1$ divided by $\frac{1}{4^3}$ , which is the same as multiplying by the reciprocal. $\newline$ $\frac{1}{\frac{1}{4^3}} = 1 \times 4^3$
Perform multiplication: Perform the multiplication to get the final answer. $\newline$ $1 \times (4^3) = 4^3$
Calculate final answer: Calculate the value of $4^3$ . $\newline$ $4^3 = 4 \times 4 \times 4 = 64$