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To simplify the expression (1/32)3(1/32)3, you raise the base to the power of the exponent:

(1/32)3=13/323(1/32)3=13/323

13=113=1

323==32768

So,

(1/32)3=1/32768(1/32)3=1/32768

Therefore, (1/32)3(1/32)3 simplifies to 1/327681/32768.

To evaluate the expression (5−1×82)/(2−3×10−1)(5−1×82)/(2−3×10−1), follow the order of operations (PEMDAS/BODMAS):

1. Exponents and Roots
2. Multiplication and Division (from left to right)
3. Addition and Subtraction (from left to right)

Let's calculate step by step:

5−1×82=5−1×64=5−64=−595−1×82=5−1×64=5−64=−59

2−3×10−1=2−3×0.1=2−0.3=1.72−3×10−1=2−3×0.1=2−0.3=1.7

Now, substitute these results back into the original expression:

−591.71.7−59

Finally, divide −59−59 by 1.71.7:

−591.7≈−34.705882351.7−59≈−34.70588235

So, the value of the given expression is approximately −34.71−34.71.

To find the value of mm in the equation 6m6−3=656−36m=65, follow these steps:

1. Simplify the expression on the left side:

   6m6−3=6m3=2m6−36m=36m=2m

2. Now, set up the equation:

   2m=652m=65

3. Solve for mm:

   m=652m=265

So, the value of mm for which 6m6−3=656−36m=65 is m=652m=265 or m=32.5m=32.5.

Let's simplify the expression step by step:

[(12−1)−(13−1)]−1[(21−1)−(31−1)]−1

First, perform the operations inside each set of parentheses:

[(12−1)−(13−1)]−1[(21−1)−(31−1)]−1

[(12−22)−(13−33)]−1[(21−22)−(31−33)]−1

[(−12)−(−23)]−1[(2−1)−(3−2)]−1

Now, combine the terms inside the brackets:

[−12+23]−1[2−1+32]−1

To add the fractions, find a common denominator, which is 6:

[−36+46]−1[6−3+64]−1

[16]−1[61]−1

Finally, take the reciprocal of 1661:

116=6611=6

Therefore, [(12−1)−(13−1)]−1=6[(21−1)−(31−1)]−1=6

To simplify (−3)5×(53)5(−3)5×(35)5, let's break it down step by step:

1. Evaluate (−3)5(−3)5:

   (−3)5=−3×−3×−3×−3×−3=−243(−3)5=−3×−3×−3×−3×−3=−243

2. Evaluate (53)5(35)5:

   (53)5=5535==3555=

Now, multiply the results:

(−243)×(−243)×

The 243243 in the numerator and denominator cancels out:

(−243)×=−243×3125(−243)×=−243×3125

Now, calculate the product:

−243×3125=−−243×3125=

Therefore, (−3)5×(53)5(−3)5×(35)5 simplifies to −]−]