Question

help me pls with these equations​

Answer 1

Answer:

The answer is 15625/117649.

Step-by-step explanation:

Simplify :

$= \Bigg[ \left\{ \bigg( \dfrac{5}{7} \bigg)^{2} \right\}^{ - 1} \Bigg]^{ - 3}$

$\begin{gathered}\end{gathered}$

Solution :

To solve this equation. We'll use law of exponent rule : (aᵐ)ⁿ = aᵐⁿ

$= \Bigg[ \left\{ \bigg( \dfrac{5}{7} \bigg)^{2} \right\}^{ - 1} \Bigg]^{ - 3}$

$= \Bigg[ \left\{ \bigg( \dfrac{5}{7} \times \dfrac{5}{7} \bigg) \right\}^{ - 1} \Bigg]^{ - 3}$

$= \Bigg[ \left\{ \bigg( \dfrac{5 \times 5}{7 \times 7}\bigg) \right\}^{ - 1} \Bigg]^{ - 3}$

$= \Bigg[ \left\{ \bigg( \dfrac{25}{49}\bigg) \right\}^{ - 1} \Bigg]^{ - 3}$

Simplifying and opening round brackets.

$= \Bigg[ \left\{ \bigg( \dfrac{25}{49}\bigg) \right\}^{ - 1} \Bigg]^{ - 3}$

$= \Bigg[ \left\{\dfrac{25}{49}\right\}^{ - 1} \Bigg]^{ - 3}$

Using the law of exponent. (aᵐ)ⁿ = aᵐⁿ

$= \Bigg[ \left\{\dfrac{25}{49}\right\}^{ - 1} \Bigg]^{ - 3}$

$= \Bigg[ \left\{\dfrac{25}{49}\right\}^{ (- 1 \times - 3)} \Bigg]$

$= \Bigg[ \left\{\dfrac{25}{49}\right\}^{3} \Bigg]$

Simplifying and opening the curly brackets.

$= \Bigg[\dfrac{25}{49} \times \dfrac{25}{49} \times \dfrac{25}{49} \Bigg]$

$= \Bigg[ \dfrac{25 \times 25 \times 25}{49 \times 49 \times 49}\Bigg]$

$= \Bigg[\dfrac{625 \times 25}{2401 \times 49}\Bigg]$

$= \Bigg[\dfrac{15625}{117649}\Bigg]$

Simplifying and opening square brackets.

$= \Bigg[\dfrac{15625}{117649}\Bigg]$

$={\underline{\underline{\red{\dfrac{15625}{117649}}}}}$

Hence, the answer is 15625/117649.

$\rule{220pt}{2.5pt}$

Learn More :

✧ Algebraic identities:-

⠀⇢ (a+b)²+(a-b)² = 2a²+2b²

⠀⇢ (a+b)²-(a-b)² = 4ab

⠀⇢ (a+b)(a -b) = a²-b²

⠀⇢ (a+b+c)² = a²+b²+c²+2ab+2bc+2ca

⠀⇢ (a-b)³ = a³-b³-3ab(a-b)

⠀⇢ (a³+b³) = (a+b)(a²-ab+b²)

⠀⇢ a²+b² = (a+b)²-2ab

⠀⇢ a³-b³ = (a-b)(a²+ab +b²)

⠀⇢ If a + b + c = 0 then a³ + b³ + c³ = 3abc

✧ BODMAS :

↝ BODMAS rule is an acronym used to remember the order of operations to be followed while solving expressions in mathematics.

It stands for :-

⠀ »» B - Brackets,

⠀ »» O - Order of powers or roots,

⠀ »» D - Division,

⠀ »» M - Multiplication 

⠀ »» A - Addition

⠀ »» S - Subtraction.

↝ It means that expressions having multiple operators need to be simplified from left to right in this order only.

✧ BODMAS RULE :

↝ First, we solve brackets, then powers or roots,then division or multiplication (whatever comes first from the left side of the expression), and then at last subtraction or addition.

⠀ ↠ Addition (+)

⠀ ↠ Subtraction (-)

⠀ ↠ Multiplication (×)

⠀ ↠ Division (÷)

⠀ ↠ Brackets ( )

✧ EXPONENT :

↝ The exponent of a number says how many times to use the number in a multiplication.

✧ LAW OF EXPONENT :

The important laws of exponents are given below:

⠀ ➠ ${\rm{{a}^{m} \times {a}^{n} = {a}^{m + n}}}$

⠀ ➠ ${\rm{{a}^{m}/{a}^{n} = {a}^{m - n}}}$

⠀ ➠ ${\rm{({a}^{m})^{n} = {a}^{mn}}}$

⠀ ➠ ${\rm{{a}^{n}/{b}^{n} = ({a/b})^{n} }}$

⠀ ➠ ${\rm{{a}^{0} = 1}}$

⠀ ➠ ${\rm{{a}^{ - m} = {1/a}^{m}}}$

⠀ ➠ ${\rm{{a}^{\frac{1}{n} } = \sqrt[n]{a}}}$

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