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 \( (143 \cdot 27^{-7})^{034} \) using the properties of integer exponents, we will first rewrite \( 27^{-7} \) and then simplify the entire expression.

1. Rewrite using positive exponents: \[ 27^{-7} = \frac{1}{27^7} \] Thus, \[ 143 \cdot 27^{-7} = \frac{143}{27^7} \] Now we substitute back into the original expression: \[ (143 \cdot 27^{-7})^{034} = \left(\frac{143}{27^7}\right)^{034} \]

2. Now we apply the exponent to both the numerator and the denominator: \[ \left(\frac{143}{27^7}\right)^{034} = \frac{143^{034}}{(27^7)^{034}} = \frac{143^{034}}{27^{7 \cdot 034}} = \frac{143^{034}}{27^{238}} \]

3. Since \( 034 \) is not a standard integer and seems like a typo, we will interpret \( 034 \) as \( 34 \): \[ \frac{143^{34}}{27^{238}} \]

Now the expression is now in the simplified positive exponent form.

To solve for a simplified fraction:

1. The numbers \( 143 \) and \( 27 \) do not have any common factors with respect to their base representations. Thus, \( \frac{143^{34}}{27^{238}} \) is the simplified fractional form.

Hence, the final answer is: \[ \boxed{\frac{143^{34}}{27^{238}}} \]