Is that Exponent ?

We know that $x^{pq}=(x^p)^q=(x^q)^p \quad$ and $\quad x^{p+q}=x^p\times x^q$ for any number $x,p,q$ .

Given that,

$5^{3x}=8$

$\implies (5^x)^3=2^3$

Comparing both sides -----

$5^x=\boxed{2}$

Now, we can find $5^{3+x}$ using the value of $5^x$ as follows --->

$5^{3+x}=5^3\times 5^x = 125\times 2 =\boxed{250}$

Since $5^{3x}=8$ , it must follow that $\sqrt[3]{5^{3x}}=\sqrt[3]{8} \Longrightarrow 5^{x}=2$ . Now, since $5^{3+x}=5^3 \cdot 5^x$ , everything is clear from here: $5^3 \cdot 5^x=125 \cdot 2=\boxed{250}$

{ 5 }^{ 3x } can be written as { 5 }^{ \left( x \right) { \left( 3 \right) } }

But as it is given that { 5 }^{ \left( x \right) { \left( 3 \right) } } = 8 So, { 5 }^{ x } = \sqrt [ 3 ]{ 8 } and { 5 }^{ x } = 2...

Now coming to the question... { 5 }^{ 3+x } = { 5 }^{ x } \times { 5 }^{ 3 } But, { 5 }^{ x } = 2 So, substituting the value of { 5 }^{ x }

we get { 5 }^{ 3+x } = 2 \times 125 Which equals 250...

5^{x}=2

5^{3+x}=5^{3} \times 5^{x} = 125 \times 2 = \boxed{250}

Hi all,

1st step, as 5^(3x) =8,

(5^x)^3 = 2^3

5^x = 2 , as 5^(3+x)= 5^3 . 5^x,

substitute 5 ^ x=2 into 5^3 . 5^x, 5^3 . 2 = 125 . 2=250

Thanks...