Question
which of the following is an equivalent expression to 15^0∙7^-2/(-4)^-3
only positive exponents that has been generated
only positive exponents that has been generated
Answers
GPT 3.5
To simplify the expression and keep only positive exponents, we can use the rule:
\(a^{-b} = \frac{1}{a^b}\)
Applying this rule to the expression:
\(15^0 \cdot 7^{-2} \div (-4)^{-3}\)
We have:
\(15^0 = 1\) (Any number raised to the power of 0 is equal to 1)
\(\frac{1}{7^2} = \frac{1}{49}\) (Using the rule \(a^{-b} = \frac{1}{a^b}\))
\(\frac{1}{(-4)^{-3}} = \frac{1}{\left(\frac{1}{(-4)^3}\right)} = -64\) (Applying the rule to the negative exponent)
Therefore, the simplified expression is:
\(1 \cdot \frac{1}{49} \div -64 = \frac{1}{49} \div -64 = -\frac{1}{3136}\)
\(a^{-b} = \frac{1}{a^b}\)
Applying this rule to the expression:
\(15^0 \cdot 7^{-2} \div (-4)^{-3}\)
We have:
\(15^0 = 1\) (Any number raised to the power of 0 is equal to 1)
\(\frac{1}{7^2} = \frac{1}{49}\) (Using the rule \(a^{-b} = \frac{1}{a^b}\))
\(\frac{1}{(-4)^{-3}} = \frac{1}{\left(\frac{1}{(-4)^3}\right)} = -64\) (Applying the rule to the negative exponent)
Therefore, the simplified expression is:
\(1 \cdot \frac{1}{49} \div -64 = \frac{1}{49} \div -64 = -\frac{1}{3136}\)