Question

If 7^ m *7^ 4 *7^ 3 7^ 3 =7^ 6 , find the value of m​

Answer 1

Solution:

Given That:-

$\rm \longrightarrow {7}^{m} \times {7}^{4} \times {7}^{3} \times {7}^{3} = {7}^{6}$

We know that:-

$\rm \longrightarrow {x}^{a} \times {x}^{b} \times {x}^{c} ... = {x}^{a+b+c+...}$

Therefore, we get:-

$\rm \longrightarrow {7}^{m + 4 + 3 + 3} = {7}^{6}$

$\rm \longrightarrow {7}^{m + 10} = {7}^{6}$

Comparing base, we get:-

$\rm \longrightarrow m + 10 = 6$

$\rm \longrightarrow m = - 4$

★ Therefore, the value of m satisfying the given equation is -4.

Learn More:

Laws of exponents.

If a, b are positive real numbers and m, n are rational numbers, then the following results hold.

$\rm 1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\rm 2. \: \: ({a}^{m})^{n} = {a}^{mn}$

$\rm 3. \: \: \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$\rm4. \: \: {a}^{m} \times {b}^{m} = {(ab)}^{m}$

$\rm5. \: \: \bigg(\dfrac{a}{b} \bigg)^{m} = \dfrac{ {a}^{m} }{ {b}^{m} }$

$\rm6. \: \: {a}^{ - n} = \dfrac{1}{ {a}^{n} }$

$\rm7. \: \: {a}^{n} = {b}^{n} \rightarrow a = b, n \neq0$

$\rm8. \: \: {a}^{m} = {a}^{n} \rightarrow m = n, a \neq 1$