(7–3)^8×4^3÷(2^3–2^2)^9

asked by guest
on Nov 17, 2024 at 1:24 pm



You asked:

Evaluate the expression: \(\frac{{\left( 7 - 3 \right)}^{8} \cdot {4}^{3}}{{\left( {2}^{3} - {2}^{2} \right)}^{9}}\)

MathBot Answer:

\[\frac{{\left( 7 - 3 \right)}^{8} \cdot {4}^{3}}{{\left( {2}^{3} - {2}^{2} \right)}^{9}} = 16\]

\[\begin{aligned}\frac{{\left( 7 - 3 \right)}^{8} \cdot {4}^{3}}{{\left( {2}^{3} - {2}^{2} \right)}^{9}}& = \left(7 - 3\right)^{8} \cdot 4^{3} \cdot \frac{1}{\left(2^{3} - 2^{2}\right)^{9}}\\& = 4^{8} \cdot 4^{3} \cdot \frac{1}{\left(2^{3} - 2^{2}\right)^{9}}\\& = 65536 \cdot 4^{3} \cdot \frac{1}{\left(2^{3} - 2^{2}\right)^{9}}\\& = 65536 \cdot 64 \cdot \frac{1}{\left(2^{3} - 2^{2}\right)^{9}}\\& = 65536 \cdot 64 \cdot \frac{1}{\left(8 - 2^{2}\right)^{9}}\\& = 65536 \cdot 64 \cdot \frac{1}{\left(8 - 4\right)^{9}}\\& = 65536 \cdot 64 \cdot \frac{1}{4^{9}}\\& = 65536 \cdot \frac{64}{262144}\\& = \frac{65536}{4096}\\& = 16\end{aligned}\]

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