Simplify: (i) ((2^(5))^(2)×7^(3))/(8^(3)×7)

Question

Simplify: (i)  ((2^(5))^(2)×7^(3))/(8^(3)×7)

Bytelearn · Accepted Answer

Simplify Terms Separately: Simplify the numerator and the denominator separately. The numerator is (2^5)^2 * 7^3. The denominator is 8^3 * 7.Apply Power Rule: Apply the power of a power rule to the term (2^5)^2. According to the power of a power rule, (a^b)^c = a^(b*c). So, (2^5)^2 = 2^(5*2) = 2^10.Recognize Power of 2: Recognize that 8 is a power of 2, specifically 8 = 2^3. So, 8^3 can be written as (2^3)^3. Applying the power of a power rule again, we get (2^3)^3 = 2^(3*3) = 2^9.Rewrite with Simplified Terms: Rewrite the original expression with the simplified terms. The expression now becomes (2^10 * 7^3) / (2^9 * 7).Cancel Common Terms: Cancel out common terms in the numerator and the denominator. We can cancel out 2^9 from the numerator and the denominator, leaving us with 2^(10-9) in the numerator. We can also cancel out 7 from the numerator and the denominator, leaving us with 7^(3-1) in the numerator. The expression now becomes 2^1 * 7^2.Calculate Remaining Expression: Calculate the remaining expression. 2^1 = 2 and 7^2 = 49. So, the simplified expression is 2 * 49.Multiply for Final Answer: Multiply the remaining terms to get the final answer. 2 * 49 = 98.

Simplify: $\newline$ $(i) \frac{(2^{5})^{2}\times 7^{3}}{8^{3}\times 7}$

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Simplify: $\newline$ $(i) \frac{(2^{5})^{2}\times 7^{3}}{8^{3}\times 7}$