Question

1) (6*10^2)^3*(16*10^-5)= 2 (8*10^2)^3*(12*10^-5)= 3) 0.8*(-10)^4+3*(-10)^3+78= 4) -0.7*(-10)^4-8*(-10)^2-26=

Answer 1

1). 216*10^6*16*10^-5=3456*10=34560;  2). 512*10^6*12*10^-5=6144*10=61440; 3). 0,8*10000+3*(-1000)+78=8000-3000+78=5078; 4). -0,7*10000-8*100-26= -7000-800-26= -7826.

Answer 2

Let's solve each of the expressions step by step:

1. $(6 \times 10^2)^3 \times (16 \times 10^{-5})$

First, let's simplify the exponents inside the parentheses: $6^3 \times (10^{2 \times 3}) \times 16 \times (10^{-5})$

Now, perform the calculations: $216 \times 10^6 \times 16 \times 10^{-5}$

Multiply the numbers and add the exponents: $216 \times 16 \times 10^{6 + (-5)}$

$216 \times 16 \times 10^1$

Now, multiply the remaining numbers: $3,456 \times 10^1$

The result is: $3,456 \times 10^1$ or simply $34,560$.

2. $(8 \times 10^2)^3 \times (12 \times 10^{-5})$

Again, simplify the exponents inside the parentheses: $8^3 \times (10^{2 \times 3}) \times 12 \times (10^{-5})$

Perform the calculations: $512 \times 10^6 \times 12 \times 10^{-5}$

Multiply the numbers and add the exponents: $512 \times 12 \times 10^{6 + (-5)}$

$512 \times 12 \times 10^1$

Now, multiply the remaining numbers: $6,144 \times 10^1$

The result is: $6,144 \times 10^1$ or simply $61,440$.

3. $0.8 \times (-10)^4 + 3 \times (-10)^3 + 78$

Let's deal with the exponents first: $0.8 \times (-10)^4 + 3 \times (-10)^3 + 78$

The exponents don't change the value of the number, only the sign. So, we have: $0.8 \times (-10,000) + 3 \times (-1,000) + 78$

Now, perform the calculations: $-8,000 - 3,000 + 78$

Finally, add the numbers: $-11,922$.

4. $-0.7 \times (-10)^4 - 8 \times (-10)^2 - 26$

Again, deal with the exponents first: $-0.7 \times (-10)^4 - 8 \times (-10)^2 - 26$

The exponents don't change the value of the number, only the sign. So, we have: $-0.7 \times (-10,000) - 8 \times (-100) - 26$

Now, perform the calculations: $7,000 + 800 - 26$

Finally, add the numbers: $7,774$.

So, the solutions are:

1. $34,560$
2. $61,440$
3. $-11,922$
4. $7,774$.