Question(c) $\frac{6.2^{-2}}{3^{-3}}$

Studdy Solution

STEP 1

1. The problem involves the use of negative exponents and their manipulation.
2. The expression can be simplified by converting negative exponents to positive exponents.
3. The final expression should be simplified as much as possible.

STEP 2

1. Simplify the expression $\frac{6.2^{-2}}{3^{-3}}$ by converting negative exponents to positive exponents.
2. Simplify the resulting expression by performing the arithmetic operations.

STEP 3

Rewrite the given expression $\frac{6.2^{-2}}{3^{-3}}$ by converting the negative exponents to positive exponents.
$\frac{6 \cdot 2^{-2}}{3^{-3}} = \frac{6}{2^2} \cdot 3^3$

STEP 4

Simplify $2^{-2}$ to $\frac{1}{2^2}$ and $3^{-3}$ to $\frac{1}{3^3}$ .
$\frac{6 \cdot \frac{1}{2^2}}{\frac{1}{3^3}} = \frac{6 \cdot \frac{1}{4}}{\frac{1}{27}}$

STEP 5

Rewrite the expression by multiplying by the reciprocal of the denominator.
$\frac{6 \cdot \frac{1}{4}}{\frac{1}{27}} = 6 \cdot \frac{1}{4} \cdot 27 = 6 \cdot \frac{27}{4}$

STEP 6

Simplify the arithmetic expression $6 \cdot \frac{27}{4}$ .
$6 \cdot \frac{27}{4} = \frac{6 \cdot 27}{4} = \frac{162}{4}$

STEP 7

Simplify $\frac{162}{4}$ by dividing the numerator and the denominator by their greatest common divisor (which is 2).
$\frac{162}{4} = \frac{81}{2}$
Therefore, the simplified value of the given expression is $\frac{81}{2}$ .

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