What is the simplified expression for 4 to the power of negative 3 multiplied by 3 to the power of 4 multiplied by 4 to the power of 2 whole over 3 to the power of 5 multiplied by 4 to the power of negative 2 ?
3 over 4
4 over 3
4 to the power of 2 over 3
3 to the power of 3 over 4
I'm so confused on this I just don't know can you please help me.
Very bad
Of course, I can help you with this problem.
To simplify the expression, we can use the properties of exponents. Let's break down the expression step by step:
First, let's simplify the numerator:
4 to the power of -3 can be written as 1 over 4 to the power of 3 since a negative exponent means the reciprocal of the base raised to the positive exponent. So, 4 to the power of -3 becomes 1 over 4 to the power of 3, which is equivalent to 1 over 64.
3 to the power of 4 is equal to 81.
4 to the power of 2 is equal to 16.
Now, let's simplify the denominator:
3 to the power of 5 is equal to 243.
4 to the power of -2 can be written as 1 over 4 to the power of 2 since a negative exponent means the reciprocal of the base raised to the positive exponent. So, 4 to the power of -2 becomes 1 over 4 to the power of 2, which is equivalent to 1 over 16.
Putting it all together:
The expression, 4 to the power of -3 multiplied by 3 to the power of 4 multiplied by 4 to the power of 2 whole over 3 to the power of 5 multiplied by 4 to the power of -2, can be simplified as follows:
(1/64) * 81 * 16 / 243 * (1/16)
Now, let's simplify the numerator and denominator separately:
Numerator: (1/64) * 81 * 16 = 18
Denominator: 243 * (1/16) = 243/16
Now, let's divide the numerator by the denominator to get the final simplified expression:
18 / (243/16)
To divide by a fraction, we can multiply by its reciprocal:
18 * (16/243) = 288/243
Next, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 9:
288/243 = (288/9) / (243/9) = 32/27
Therefore, the simplified expression for the given problem is 32/27.
So, the correct answer is "4 to the power of 2 over 3".
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why all the words? That's why we have math symbols
(4^-3)(3^4)(4^2) / (3^5)(4^-2)
Add powers in product, subtract powers in divisors:
4^(-3+2-(-2)) * 3^(4-5)
4^3 * 3^-1
4^3/3
I suspect a typo in the problem or in the answers.
Of course, you need to check my arithmetic, I guess...