s8impliy this exponential expression):
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To simplify the expression (-2^7 * 6^(-9))^8 * (7^(-3)) * (w^(-8)) * (x^6) * (4^(-3)), follow these steps:
Step 1: Simplify the exponents within parentheses.
(-2^7 * 6^(-9))^8 = (-128 * 1/6^9)^8
Step 2: Calculate the values within parentheses.
(-128 * 1/6^9)^8 = (-128 * 1/10,077,696)^8
Step 3: Simplify the exponents.
((-128)^8 * (1/10,077,696)^8)
Step 4: Calculate the base raised to the power of the exponent.
((-128)^8 = 2^8 * (-2)^8 = 256 * 256 = 65,536
(1/10,077,696)^8 = 1/(10,077,696^8)
Step 5: Simplify the remaining expression.
65,536 * 1/(10,077,696^8) * (7^(-3)) * (w^(-8)) * (x^6) * (4^(-3))
Therefore, the simplified expression is 65,536 * 1/(10,077,696^8) * 7^(-3) * w^(-8) * x^6 * 4^(-3).
To simplify the given expression, we need to perform the calculations step by step. Let's break it down:
First, we'll simplify the exponent (-2)^7:
(-2)^7 equals -(2^7) since it has an odd exponent. We can further simplify this to -(2 * 2 * 2 * 2 * 2 * 2 * 2), which gives us -128.
Next, we'll multiply this result by the base (7):
-128 * 7 = -896.
Moving on, we'll simplify the exponent (-8)^6:
Since it has an even exponent, (-8)^6 equals (8^6). Expanding this further, we get (8 * 8 * 8 * 8 * 8 * 8), which equals 262,144.
Now, we'll multiply the previous result by this value:
-896 * 262,144 = -236,326,144.
Next, we'll simplify the exponent (-9)^8:
Since it has an even exponent, (-9)^8 equals (9^8). Expanding this further, we get (9 * 9 * 9 * 9 * 9 * 9 * 9 * 9), which equals 430,467,21.
Moving on, we'll multiply the previous result by this value:
-236,326,144 * 430,467,21 = -101,706,399,845,604,224.
Finally, let's simplify the base (4) to the power of (-3):
Since it has a negative exponent, (4)^(-3) equals 1 / (4^3). Expanding this, we get 1 / (4 * 4 * 4), which is equal to 1 / 64.
Lastly, we'll multiply the previous result by this value:
-101,706,399,845,604,224 * (1 / 64) = -1,588,161,249,149,381.
Therefore, simplifying the given expression results in -1,588,161,249,149,381.