Question

x⁵.x²=? ? ? ? ? ? ? ​

Answer 1

Law's of exponents

The following product of powers rule will be used to find the solution:

$\boxed{\;\;a^m \times a^m = a^{m + m}\;\;}$

Solution:

$\implies x^5 \cdot x^2$

Since the base values are both $x$, keep them the same and then add the exponents (5 + 2) together.

$\implies x^{5 + 2}$

Perform the exponents multiplication.

$\implies x^{7}$

Hence, the correct answer is x⁷.

$\rule{90mm}{2pt}$

LAW'S OF EXPONENTS

$\boxed{\begin{array}{l}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{array}}$

Answer 2

Answer :

$\sf x^7$

Step-by-step explanation :

Given :

$\star\bf \: {x}^{5}. {x}^{2}$

To Find :

• Value of it.

Solution :

Here, point i.e. (.) means multiplication so the expression can be written as :

$\\ \implies \sf \: {x}^{2}. {x}^{5} \\ \\ \implies \underline{ \bf \: {x}^{2} \times {x}^{5} }$

Now, in order to solve we need to apply "Laws of Exponents".

★ For this question we will the law stated below :

$\color{hotpink}{ \longrightarrow \boxed{ \bf {a}^{m} \times {a}^{n} = {a}^{m + n} } \: \bigstar}$

According to the question here,

• a = x
• m = 5
• n = 2

Let's start with solving :D!

$\longrightarrow \sf \: {x}^{5} \times {x}^{2} \\ \\ \longrightarrow \sf \: {x}^{5 \: \: + 2} \\ \\ \longrightarrow \boxed{\bf \: {x}^{7} } \: \bigstar$

Hence,

$\: \: \qquad \qquad \bf \: \bull \: {x}^{5} \times {x}^{2} = \boxed{ \bf{x}^{7} }$