Math Problem Statement

Simplify or solve the given mathematical expressions, as provided in the image.

Solution

The problem consists of simplifying or solving the expressions provided in the image. Let’s tackle each of the expressions systematically:


Expression A:

A=812×82×121212522×147A = \frac{81^2 \times 8^2 \times 121^2}{1252^2 \times 147}

We'll simplify 812,82,1212,1252281^2, 8^2, 121^2, 1252^2, and compute the division.


Expression B:

B=0.0081×(0.0021)2×25633202×(0.0064)5B = \frac{0.0081 \times (0.0021)^2 \times 256^3}{320^2 \times (0.0064)^5}

This involves simplifying decimal powers and large integer powers, then performing the multiplication and division.


Expression C:

C=3.072144×0.125×21632562×0.0081C = \frac{3.072144 \times 0.125 \times 216^3}{256^2 \times 0.0081}

We'll compute powers 2163216^3 and 2562256^2, followed by the multiplications and division.


Expression D:

D=257×11024×815×2D = 25^7 \times \frac{1}{1024} \times 81^5 \times 2

Here, simplify 257,81525^7, 81^5, and perform the multiplications with 11024\frac{1}{1024} and 2.


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Math Problem Analysis

Mathematical Concepts

Exponents and Powers
Simplification of Expressions
Order of Operations (BODMAS)

Formulas

Laws of Exponents: a^m * a^n = a^(m+n), (a^m)^n = a^(m*n)
Simplification: Fractions and decimals

Theorems

Basic properties of exponents
Arithmetic operations on fractions and decimals

Suitable Grade Level

Grades 9-12