Question

find value of( 1296)^0.17*(1296)^0.08

Answer 1

Hey friend,
${1296}^{0.17} \times {1296}^{0.08} \\ \\ using \: the \: identity \\ {a}^{m} \times {a}^{n} = {a}^{m + n} \\ \\ = {1296}^{0.17 + 0.08} \\ \\ = {1296}^{0.25} \\ \\ = { {(6}^{4}) }^{ \frac{25}{100} } \\ \\ = {6}^{4 \times \frac{25}{100} } \\ \\ = {6}^{ \frac{25}{25} } \\ \\ = {6}^{1} \\ \\ = 6$


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@Mahak24

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Answer 2

Answer:

The simplified value of the expression is 6.

Step-by-step explanation:

The given expression which needs to be simplify is

$(1296)^{0.17}\cdot(1296)^{0.08$

We know that if base is same then we can add the exponents. The exponent formula is

$x^a\cdotx^b=x^{a+b}$

Using this rule, we can write the expression as

$(1296)^{0.17+0.08}$

This can be further simplified as

$(1296)^{0.25}$

Now the base 1296 can be written as $6^4$

$(6^4)^{0.25}$

Using the exponent rule $(x^a)^b=x^{ab}$

$(6)^{4\cdot0.25}$

This can be simplified as

$(6)^{1}\\\\=6$

Therefore, the simplified value of the expression is 6.