Explain---Page Number: 4 Question Number: 11 Mathematical Equation: $m^{-\frac{1}{4}} = 27m^{-1}$ Question Stem: Find the value of m. Answer Space: $m = \text{..........................................}$ Marks: [3]

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Now we'll use the quotient rule for exponents. When dividing powers with the same base, we subtract the exponents. So m divided by m to the one-fourth becomes m to the power of one minus one-fourth, which equals m to the three-fourths. To solve for m, we raise both sides to the power of four-thirds. Now we need to evaluate 27 to the power of four-thirds. We can rewrite this as 27 to the one-third, raised to the fourth power. 27 to the one-third is the cube root of 27, which equals 3. Then 3 to the fourth power equals 81. Therefore, m equals 81. Let's verify our answer by substituting m equals 81 back into the original equation. The left side becomes 81 to the negative one-fourth, which equals one-third. The right side becomes 27 times 81 to the negative first, which also equals one-third. Since both sides are equal, our answer m equals 81 is correct.