Question

Can someone please help me with this???
Brainlyest if you help me.

Find the value of the following expression:

(28 • 5–5 • 190)–2 • (the image is in the file) • 228 (5 points)

Write your answer in simplified form. Show all of your steps. (5 points)

Answer 1

Answer:

$\left(\dfrac{5^{-2}}{2^3}\right)^4$

$\dfrac{\left(5^{-2}\right)^4}{\left(2^3\right)^4}$

$\dfrac{\left(5^{-8}\right)}{\left(2^{12}\right)^}$

$\dfrac{\dfrac{1}{390625}}{4096}$

$\dfrac{1}{390625} *\dfrac{1}{4096}$

$\dfrac{1}{1600000000}$

$\left\mathrm{In \ decimal \ or \ standard \ form :\quad }\:6.25E-10\right$

Answer 2

Solution:

$\large\tex\text{Given expression:} \huge\tex\text{[}\dfrac{5^{-2} }{2^{3} } \huge\tex\text{]}^{4}$

Since the exponents inside the brackets do not have any relation (Not through bases, nor through exponents), we will need to simplify the exponents.

1. Simplifying the exponents inside the bracket:

$\bullet \ \rightarrow \huge\tex\text{[}\dfrac{5^{-2} }{2^{3} } \huge\tex\text{]}^{4}$

$\bullet \ \rightarrow \huge\tex\text{[}\dfrac{\frac{1}{5^{2} } }{2 \times 2 \times 2} \huge\tex\text{]}^{4}$

$\bullet \ \rightarrow \huge\tex\text{[}\dfrac{\frac{1}{25 } }{8} \huge\tex\text{]}^{4}$

2. Opening the brackets:

$\bullet \ \rightarrow \huge\tex\text{[}\dfrac{\frac{1}{25 } }{8} \huge\tex\text{]}^{4}$

$\bullet \ \rightarrow \huge\tex\text{[}\dfrac{\frac{1^{4} }{25^{4} } }{8^{4} } \huge\tex\text{]}$

$\bullet \ \rightarrow \dfrac{\frac{1^{4} }{25^{4} } }{8^{4} }$

3. Simplifying the exponents:

$\bullet \ \rightarrow \dfrac{\frac{1^{4} }{25^{4} } }{8^{4} }$

$\bullet \ \rightarrow \dfrac{\dfrac{1}{390625 } }{4096}$

$\bullet \ \rightarrow {\dfrac{1}{390625 } \times \dfrac{1}{4096}$

$\bullet \ \rightarrow \boxed{\bold{\dfrac{1}{1600000000} }}$