Question

If x=(5/4)^5 ÷ (5/4)^3 find x^2​

Answer 1

ɢɪᴠᴇɴ:

• x = (5/4)⁵ ÷ (5/4)³.

ᴛᴏ ғɪɴᴅ:

• The value of x².

ᴀɴsᴡᴇʀ:

Before we proceed lets us have a look at the laws of exponents:

• ${\underline{\red{\bf{a^m\times a^n=a^{m+n}}}}}$
• ${\underline{\red{\bf{a^m\div a^n=a^{m-n}}}}}$
• ${\underline{\red{\bf{a^m\times b^m=(a\times b)^{m}}}}}$
• ${\underline{\red{\bf{ a^0=1}}}}$

Now lets procced ,

Given that x = (5/4)⁵ ÷ (5/3)³

Now here we can see that the bases are same but the powers are different .So we will use the formula $\bf{a^m \div a^n = a^{m-n}}$ .

This becomes

$\red{\bf{=\dfrac{5}{4}^5 \div \dfrac{5}{4}^3}}$

$\red{\bf{= \dfrac{5}{4}^{(5-3)}}}$

$\red{\bf{=(\dfrac{5}{4})^2}}$

$\underline{\boxed{\purple{\bf{=\dfrac{25}{16}}}}}$

Hence we got the value of x as 25/16.

Therefore x²

= $\red{\sf{(\dfrac{25}{16})^2}}$

$\red{\bf{=\dfrac{625}{256}}}$

Hence the required answer is 625/256.