Solve (1/9)^?*(4/5)^?=(4/45)^2

$$( \frac { 1 } { 9 } ) ^ { ? } \cdot ( \frac { 4 } { 5 } ) ^ { ? } = ( \frac { 4 } { 45 } ) ^ { 2 }$$

Verify

Solution Steps

Calculate \frac{1}{9} to the power of 1 and get \frac{1}{9}.

$$\frac{1}{9}\times \left(\frac{4}{5}\right)^{1}=\left(\frac{4}{45}\right)^{2}$$

Calculate \frac{4}{5} to the power of 1 and get \frac{4}{5}.

$$\frac{1}{9}\times \frac{4}{5}=\left(\frac{4}{45}\right)^{2}$$

Multiply \frac{1}{9} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{9\times 5}=\left(\frac{4}{45}\right)^{2}$$

Do the multiplications in the fraction \frac{1\times 4}{9\times 5}.

$$\frac{4}{45}=\left(\frac{4}{45}\right)^{2}$$

Calculate \frac{4}{45} to the power of 2 and get \frac{16}{2025}.

$$\frac{4}{45}=\frac{16}{2025}$$

Least common multiple of 45 and 2025 is 2025. Convert \frac{4}{45} and \frac{16}{2025} to fractions with denominator 2025.

$$\frac{180}{2025}=\frac{16}{2025}$$

Compare \frac{180}{2025} and \frac{16}{2025}.

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