Apply the Properties of Integer Exponents to generate equivalent expressions to (143⋅27−7)034

Question

with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(143⋅27−7)034=

Answer 1

To simplify the expression \((143 \cdot 27^{-7})^{034}\), we first need to rewrite the expression to avoid negative exponents.

1. We can express \(27^{-7}\) as \(\frac{1}{27^7}\). Thus, we have: \[ 143 \cdot 27^{-7} = 143 \cdot \frac{1}{27^7} = \frac{143}{27^7} \]

2. Now, we raise this entire fraction to the power of \(034\) (which is the same as \(34\)): \[ \left(\frac{143}{27^7}\right)^{34} \]

3. Using the property of exponents \((\frac{a}{b})^n = \frac{a^n}{b^n}\), we can separate the numerator and the denominator: \[ = \frac{143^{34}}{(27^7)^{34}} \]

4. Apply the exponent to the denominator: \[ = \frac{143^{34}}{27^{7 \cdot 34}} = \frac{143^{34}}{27^{238}} \]

Thus, the simplified fraction with no remaining exponents is: \[ \frac{143^{34}}{27^{238}} \]

This is the final answer.